Two-dimensional photonic crystal optical multiplexer/demultiplexer using boundary reflection

ABSTRACT

In an in-plane heterostructure photonic crystal in which vacancies  32  are periodically arranged in each of forbidden band zones  301, 302,  with different cycle distances, a waveguide  33  is formed passing through all the forbidden band zones and point-like defects  341, 342, . . .  are formed in each of the forbidden band zones. Since, of all light propagating through the waveguide from the light introduction/take-out section  36  and having the frequency  52  demultiplexed from the predetermined point-like defect, the wavelength of light passing through the predetermined point-like defect is not included in transmission bands  51  of the waveguide in the adjacent forbidden band zone, so that the light is reflected on the boundaries  351  and  352  between forbidden band zones and introduced into the point-like defect. Thereby, the demultiplexing efficiency of light is improved. The same applies to the multiplexing efficiency.

TECHNICAL FIELD

The present invention relates to a two-dimensional photonic crystaloptical multiplexing/demultiplexing device used for wavelength divisionoptical multiplex communication or the like. Particularly, the presentinvention relates to a technique for improving themultiplexing/demultiplexing efficiency.

BACKGROUND ART

Recently, a photonic crystal has been drawing attention as a new opticaldevice. The photonic crystal is a functional material having aperiodical distribution of refractive index, which provides a bandstructure with respect to the optical and electromagnetic energies.Especially, the photonic crystal is characterized by the fact that itforms an energy region (a photonic band gap) therein through whichneither light nor electromagnetic wave are impossible to propagate.

By introducing an appropriate defect in the distribution of refractiveindex in the photonic crystal, an energy level belong to the defect(defect level) is created in the photonic band gap. In this state, onlylight with the wavelength corresponding to the energy of the defectlevel can be present in the wavelength band corresponding to theenergies in the photonic band gap. Defects arranged in a line in aphotonic crystal constitute a waveguide, while a point-like defect in aphotonic crystal works as a resonator.

A photonic crystal can be a two-dimensional crystal or athree-dimensional crystal. Though either of the crystals has respectiveadvantages, the two-dimensional crystal is advantageous in that thecrystal is comparatively easy to manufacture. In Japanese UnexaminedPatent Application No. 2001-272555, it is described that, in atwo-dimensional photonic crystal, a periodical distribution ofrefractive index is created by arranging cylindrical holes periodicallyin a triangular lattice pattern, that a waveguide is formed by renderingthe cylindrical holes defective in a linear arrangement ([0025] and FIG.1), and that a point defect is formed in the vicinity of the waveguide([0029] and FIG. 1). Further, in Japanese Unexamined Patent ApplicationNo. 2001-272555, a point defect created by increasing the diameter of acylindrical hole among those periodically arranged has been described asan example.

The applicants of the present application have proposed, in JapaneseUnexamined Patent Application No. 2003-279764, to create a clusterdefect by rendering defects in two or more adjoining modified refractiveindex areas among those constituting the periodical distribution ofrefractive index. A defect of the modified refractive index area iscreated by rendering the refractive index of a modified refractive indexarea different from that of other modified refractive index areas. Inthis construction, a defect of a modified refractive index area whoserefractive index is lower than that of other modified refractive indexareas is called an acceptor type defect, and a defect of a modifiedrefractive index area whose refractive index is higher than that ofother modified refractive index areas is called a donor type defect. Adefect created by enlarging a cylindrical hole, which is described inJapanese Unexamined Patent Application No. 2001-272555, is an acceptortype defect, and a defect created by providing no modified refractiveindex area is a donor type defect. A cluster defect, and a point defectcreated by rendering only one modified refractive index area defective,are collectively referred to as “point-like defect”.

In Japanese Unexamined Patent Application No. 2003-279764 mentionedabove, the applicants of the present application have proposed atwo-dimensional photonic crystal with an in-plane heterostructure thathas plural forbidden band zones each having modified refractive indexareas with a different cycle distance from one another, where, in eachof the zones, a point-like defect is created. With such a construction,when point-like defects in the same shape are provided in the respectiveforbidden band zones, lights with different wavelengths can be resonatedat respective point-like defects due to differences in the cycledistance of the modified refractive index areas.

A variety of applications can be thought of the two-dimensional photoniccrystal having such point-like defects. As a typical example, an opticalmultiplex communication can be shown. For the optical multiplexcommunication of recent years, the wavelength-division multiplexingscheme is adopted, in which lights with plural wavelengths each carryingrespective signal are propagated along a single transmission line. Atwo-dimensional photonic crystal, by providing plural point-like defectscorresponding to respective wavelengths in the vicinity of a waveguide,can be used as a demultiplexer for taking out lights (signals) withspecific wavelengths out of lights propagating in the waveguide from thepoint-like defects, or alternatively, as a multiplexer for introducinglights with specific wavelengths into the waveguide from the point-likedefects.

In the case where a conventional two-dimensional photonic crystaldescribed above is used as a demultiplexer, the demultiplexingefficiency will be 100% if, among lights passing through the waveguide,all of light with the wavelength to be demultiplexed flows into thepoint-like defect. However, actually, more than 50% of the light withwavelength to be demultiplexed passes over the waveguide without flowinginto the point-like defect. Hence, an actual demultiplexing efficiencyis 50% or less.

In the case where the two-dimensional photonic crystal is used as amultiplexer, when the light to be multiplexed flows into the waveguidefrom a point-like defect, the light is divided into two ways of thewaveguide. Therefore, the take-out efficiency of multiplexed light fromthe waveguide is 50% at the highest.

The present invention has been made in order to solve such problems, andit is an object of the present invention to provide a two-dimensionalphotonic crystal optical multiplexer/demultiplexer with highmultiplexing efficiency and demultiplexing efficiency.

DISCLOSURE OF THE INVENTION

To solve the aforementioned problems, in the first mode of the presentinvention, a two-dimensional photonic crystal opticalmultiplexer/demultiplexer using boundary reflection includes:

a) a slab-shaped body;

b) plural modified refractive index areas arranged periodically in thebody, each having a refractive index different from that of the body;

c) a waveguide formed by creating defects of the modified refractiveindex areas in a linear arrangement;

d) a point-like defect formed by creating a defect of modifiedrefractive index area in the vicinity of the waveguide; and

e) a first reflecting section provided at an end of the waveguide, andreflecting at least part of light with the resonant wavelength of thepoint-like detect.

In the second mode of the present invention, a two-dimensional photoniccrystal optical multiplexer/demultiplexer using boundary reflectionincludes:

a) a slab-shaped body;

b) two or more forbidden band zones provided in the body;

c) plural modified refractive index areas provided in each of theforbidden band zones, each area having a refractive index different fromthat of the body, and periodically arranged in the body in a differentcycle distance from each other in each of the forbidden band zones;

d) a waveguide formed by creating defects of modified refractive indexareas in a linear arrangement in the respective forbidden band zones,and passing through all the forbidden band zones;

e) a point-like defect created in the vicinity of the waveguide in eachof the forbidden band zones; and

f) a first reflecting section provided at an end of the waveguide, andreflecting at least part of light with the resonant wavelength of thepoint-like defect,

wherein,

g) a part of a waveguide-transmittable wavelength band in each of theforbidden band zone is not included in a waveguide-transmittablewavelength band of all forbidden band zones present on the side of thefirst reflecting section from the forbidden band zone, but included inthe waveguide-transmittable wavelength band of all forbidden band zonespresent on the side opposite to the first reflecting section from theforbidden band zone; and

h) the resonant wavelength of the point-like defect created in each ofthe forbidden band zones is included in the part of the transmissionwavelength band.

The two-dimensional photonic crystal optical multiplexer/demultiplexerusing boundary reflection disclosed in the present invention uses atwo-dimensional photonic crystal as the matrix, where the matrix iscomposed of a slab as the body, where the thickness of the slab issufficiently smaller than its size in the in-plane direction, and areashaving refractive index different from that of the body are arrangedperiodically in the body. In the two-dimensional photonic crystal as thematrix, a photonic band gap is created in the presence of the modifiedrefractive index areas periodically arranged, and light havingcorresponding energies is not allowed to be present. That is, light inwavelength bands corresponding to the photonic band gap cannot passthrough the body. Materials of the body that can be used include, forexample, Si and InGaAsP. A modified refractive index area is an areacreated by placing a member in the body made from a material havingrefractive index different from that of the material of the body. Atypical example is a cylindrical hole as described in JapaneseUnexamined Patent Application No. 2001-272555. If a cylindrical hole isadopted, what is required is to form a hole in the body, and the holecan be fabricated easier than placing a certain member in the body.

A defect formed in a part of the modified refractive index areasdisturbs the periodicity of the crystal lattice. By appropriatelysetting parameters, such as the refractive index or the size of thedefect, a defect level is created in the photonic band gap, and lightwith the wavelength corresponding to the energy of the defect level canbe present at the position of the defect. By forming defectssuccessively in a linear arrangement, a waveguide is created that cantransmit light of a certain wavelength range in the photonic band gap.This waveguide guides multiplexed light including plural wavelengthcomponents before demultiplexing at an optical demultiplexer or aftermultiplexing at an optical multiplexer. The multiplexed light isintroduced from an end of the waveguide in the case of an opticaldemultiplexer, and taken out from an end of the waveguide in the case ofan optical multiplexer.

A point-like defect is provided in the vicinity of a waveguide. Thepoint-like defect may be either a point defect or a cluster defect. Thedefect of a modified refractive index area, which may be a point defector a cluster defect, may be either of the acceptor type or of the donortype mentioned before. By appropriately setting parameters, such as thekind, the size or the position, of a point-like defect, a desired defectlevel is created in a photonic band gap, and only light with thewavelength corresponding to the energy of the detect level resonates atthe detect. In the case of an optical demultiplexer, among multiplexedlight including plural wavelength components propagating through thewaveguide, light with the resonant wavelength of the point-like defectis introduced from the waveguide into the point-like defect, and then istaken outside from the point-like defect. In the case of an opticalmultiplexer, light with the resonant wavelength of the point-like defectis introduced into the waveguide from the outside through the point-likedefect.

The construction having discussed above that a waveguide and point-likedefects are provided in a two-dimensional photonic crystal as the matrixis the same as those proposed in Japanese Unexamined Patent ApplicationNos. 2001-272555 and 2003-279764. The present invention further includesa construction that reflection of at least a part of light with apredetermined wavelength occurs at the end opposite to the end of thewaveguide where the multiplexed light is introduced into or taken outfrom. The end of the waveguide is referred to as the first reflectingsection.

A typical example of the first reflecting section includes aconstruction in which the waveguide extends as far as an end of thetwo-dimensional photonic crystal body. With the construction, if the endof the body is in contact with the ambient space, the crystal isdiscontinuous in the lattice structure at the body end, and a part oflight is reflected at the end of the waveguide reaching the end of thebody. That is, the end of the waveguide serves as the first reflectingsection without providing a special light reflecting member.

Another example of the first reflecting section is a construction that awaveguide is, in the same way as described above, formed in atwo-dimensional photonic crystal so as to reach as far as an end of thebody of the photonic crystal, to which end is connected anothertwo-dimensional photonic crystal that does not transmit light with theresonant wavelength of the point-like defect. With this construction,the end of the waveguide serves as the first reflecting sectionreflecting all of light with the resonant wavelength of the point-likedefect.

In the case of an optical demultiplexer with the above construction, oflight with the resonant wavelength corresponding to the point-likedefect propagating the waveguide, light passing over the point-likedefect without being introduced is reflected on the first reflectingsection, and returns to the point-like defect. Therefore, the intensityof light without being introduced into the point-like defect and endingup with a loss decreases compared to a conventional case, whereby theoptical demultiplexing efficiency is improved. On the other hand, in thecase of an optical multiplexer, of light introduced into the waveguidefrom the point-like defect, light propagating toward the end opposite tothe end of the waveguide where light is taken out is reflected on thefirst reflecting section, and returns to the end of the waveguide wherelight is taken out. Therefore, the intensity of light that is lost atthe end opposite to the end of the waveguide where light is taken outdecreases compared to a conventional case, whereby the opticalmultiplexing efficiency is improved.

By appropriately setting the distance between the point-like defect andthe first reflecting section, the demultiplexing efficiency or themultiplexing efficiency can be further increased. In the case of anoptical demultiplexer, a reflection loss also occurs by the reflectionof light at the point-like defect with the resonant wavelength of thepoint-like defect. Hence, it is desirable to set the distance betweenthe point-like defect and the first reflecting section so that lightreflected on the first reflecting section and light reflected on thepoint-like defect are attenuated by interference, or the phasedifference of the two lights takes the value of π. Therefore, the twolights are both difficult to be present, and the intensity of lightdemultiplexed from the point-like defect increases, which means that thedemultiplexing efficiency is improved. Note that the phase of lightreflected on the point-like defect is reversed, while the phase of lightreflected on the first reflecting section changes in a different wayaccording to the construction of the first reflecting section. Forexample, in the case where the first reflecting section is constitutedof the boundary between the slab and the air, no change occurs in thephase of light reflected on the boundary. Hence, in order to increasethe demultiplexing/multiplexing efficiency, it is desirable to set thedistance between the point-like defect and the first reflecting sectionto the value n/2 times the resonant wavelength of the point-like defect(where n is a positive integer, which applies in the descriptionhereinafter). On the other hand, in the case where the first reflectingsection is made of a metal surface, the phase of light reflected thereonis reversed. In this case, it is desirable to set the distance to thevalue (2n−1)/4 times the resonant wavelength of the point-like defect.

In the case of an optical multiplexer, it is desirable to set thedistance between the point-like defect and the first reflecting sectionso that, of all the light introduced into the waveguide from thepoint-like defect, light propagating directly toward the end of thewaveguide where light is taken-out, and light reflected on the firstreflecting section are intensified by interference, that is, the phasedifference between the two lights is 0. As a result, the multiplexingefficiency is improved. Since the phase of light propagating directlytoward the end of the waveguide does not change, and the phase of lightreflected at the first reflecting section becomes as described above, itis desirable to set the distance to the value n/2 times the resonantwavelength of the point-like defect in the case where the firstreflecting section is constituted of the boundary between the slab andthe air, while in the case where the first reflecting section isconstituted of a metal surface, it is desirable to set the distance tothe value (2n−1)/4 times the resonant wavelength of the point-likedefect.

In the case of an optical demultiplexer, the demultiplexing efficiencycan be improved by providing a second reflecting section reflecting atleast part of light with the resonant wavelength of the point-likedefect at the end of the waveguide opposite to the first reflectingsection. Such a second reflecting section can be constructed, forexample, by extending the waveguide as far as an end of thetwo-dimensional photonic crystal body. Improvement of the demultiplexingefficiency in this case is due to the phenomenon that light reflected onthe first reflecting section and the point-like defect is furtherreflected on the second reflecting section and then introduced into thepoint-like defect. Moreover, it is desirable to set the distance betweenthe point-like defect and the second reflecting section to the valuewhere light introduced into the waveguide and propagating toward thepoint-like defect, and light reflected on the point-like defect and thefirst reflecting section and further reflected on the second reflectingsection are intensified by interference, that is, the phase differencebetween the two lights is 0. Thereby, the demultiplexing efficiency isfurther improved.

The demultiplexing efficiency of an optical demultiplexer also dependson the Q value, which is a coupling coefficient between a point-likedefect and an external optics. Q-value is a value representing thesharpness as a resonator of the point-like defect, which is defined byQ=ω_(t)×E₀/E₁, where ω_(t) is the resonant frequency (angular frequency)of the resonator, E₀ is the energy accumulated in the resonator, and E₁is the energy lost in a unit time due to coupling with the externaloptical modes. A higher Q-value is desirable in a resonator sincefrequency selectivity (or frequency resolution) increases. In contrastto that, in the case of an optical demultiplexer, since light should bedemultiplexed efficiently into the free space from the waveguide, inaddition to the requirement of high frequency selectivity, it isnecessary to appropriately set the coupling coefficient Qp between thepoint-like defect and the waveguide and the coupling coefficient Qvbetween the point-like defect and the air. For example, in the casewhere no reflection occurs on an end of a waveguide, the demultiplexingefficiency takes the maximum value if Qp=Qv, and its value is 50% asdescribed above.

In the case where light with the resonant wavelength of the point-likedefect is totally reflected on the first reflecting section, thedemultiplexing efficiency η is obtained by the following equation (1)based on the mode coupling equation.

$\begin{matrix}{{\eta = \frac{2Q_{p}Q_{v}{{1 - {\exp\left( {{- 2}j\;\beta\; L} \right)}}}^{2}}{{{Q_{p} + {Q_{v}\left( {1 - {\exp\left( {{- 2}j\;\beta\; L} \right)}} \right)}}}^{2}}},} & (1)\end{matrix}$where L is the distance between the point of the waveguide nearest tothe point-like defect and the first reflecting section. β is thepropagation constant of the waveguide as defined by β=2π/λ′ using thewavelength λ′ of light in the waveguide. When L is determined so thatthe phase difference between light reflected on the first reflectingsection and light reflected on the point-like defect becomes π asdescribed above, exp(−2jβL)=−1 is established. In this case, thedemultiplexing efficiency η is

$\begin{matrix}{\eta = {\frac{8Q_{p}Q_{v}}{{{Q_{p} + {2Q_{v}}}}^{2}}.}} & (2)\end{matrix}$In equation (2), if Qp/Qv is set in the range of 1.4 to 2.8, thedemultiplexing efficiency is 97% or more, where the loss is actuallynegligible. In the case where Qp/Qv=2, the demultiplexing efficiency is100%, wherein light with a predetermined wavelength in the waveguide canbe demultiplexed without loss owing to the point-like defect.

In a conventional two-dimensional photonic crystal opticaldemultiplexer, the maximum value of demultiplexing efficiency was 50%obtained in the case where Qp/Qv=1 as described above. The presentinvention makes it possible to obtain 100% as the maximum value ofdemultiplexing efficiency in a two-dimensional photonic crystal opticaldemultiplexer. Even in the case where Qp/Qv=1, the demultiplexingefficiency in the optical demultiplexer of the present invention can be88%, and this value is higher than that in conventional cases.

The above-described conditions for controlling the demultiplexingefficiency include only parameters relating to the point-like defect andthe part of the waveguide from the point nearest to the point-likedefect and the first reflecting section. On the other hand, no specificlimitation is placed on parameters with respect to the other part of thewaveguide opposite to the first reflecting section, such as the distancebetween the end of the waveguide opposite to the first reflectingsection and the point nearest to the point-like defect, or thereflectance of light on the end of the waveguide.

In order to obtain a higher demultiplexing efficiency by controlling theratio of Qp to Qv, the value of Qp can, for example, be controlled byadjusting the distance between the point-like defect and the waveguide.The value of Qp can also be controlled by adjusting the width of thewaveguide. While the resonant wavelength slightly changes with the aboveadjustments, the magnitude of the change is so small that the change ispractically negligible. Even in the case where the change in theresonant wavelength is not negligible, the resonant wavelength can bereadjusted with the ratio of Qp to Qv being kept unchanged by adjustingthe cycle distance in the modified refractive index areas.

Then, description the second mode of the present invention of atwo-dimensional photonic crystal optical multiplexer/demultiplexer usingboundary reflection is described. This two-dimensional photonic crystaloptical multiplexer/demultiplexer has an in-plane heterostructure havingbeen proposed in Japanese Unexamined Patent Application No. 2003-279764.

The body is divided into zones, where the number of zones is the same asthe number of wavelengths to be multiplexed or demultiplexed. The zoneis referred to as “forbidden band zone”. In the present invention, theforbidden band zones are arranged in ascending or descending order ofwavelength to be multiplexed or demultiplexed. Modified refractive indexareas in different cycle distances are arranged in respective forbiddenband zones.

Defects of modified refractive index areas are created successively in alinear arrangement so that the linear arrangement of the defects passesthrough all the forbidden band zones, thereby forming a waveguide. Thefirst reflecting section is provided in the same way as described beforeat the end of the waveguide opposite to the end where light isintroduced into (in the case of an optical demultiplexer) or is takenout (in the case of an optical multiplexer). Similarly to the casedescribed above, the first reflecting section can be formed by extendingthe waveguide to an end of the two-dimensional photonic crystal body, inwhich case the first reflecting section can be formed without providinga specific light-reflecting member. A two-dimensional photonic crystalthat transmits no light with the wavelength to be multiplexed ordemultiplexed may be connected to the forbidden band zone to the end ofthe body belongs.

Since the cycle distance of the modified refractive index area isdifferent among the forbidden band zones, the wavelength band of lightcapable of being transmitted through the waveguide(waveguide-transmittable wavelength band) is different according to eachforbidden band zone. As the cycle distance of the modified refractiveindex areas becomes larger, the waveguide-transmittable wavelength bandis shifted to the longer wavelength side. In the second mode, using theabove phenomenon, in the case where the forbidden band zones arearranged in ascending order of wavelength to be multiplexed ordemultiplexed toward the first reflecting section side, the cycledistance of modified refractive index areas is rendered longer in thecorresponding order, while in the case where the forbidden band zonesare arranged in descending order of wavelength to be multiplexed ordemultiplexed, the cycle distance of modified refractive index areas isrendered shorter in the corresponding order. With this construction, itis possible to include a part of the waveguide-transmittable wavelengthband in each of the forbidden band zones is included in all thewaveguide-transmittable wavelength bands belonging to the side oppositeto the first reflecting section, but is not included in thewaveguide-transmittable wavelength band of the forbidden band zoneadjacent on the first reflecting section side. In each of the forbiddenband zones, the cycle distance of modified refractive index areas isdetermined so that the part of the waveguide-transmittable wavelengthband includes the wavelength of light to be multiplexed ordemultiplexed.

A point-like defect that resonates with light of the wavelength to bemultiplexed or demultiplexed is formed in each of the forbidden bandzones. The point-like defect may be either the point defect or thecluster defect described before, and the defect of modified refractiveindex areas constituting a point defect or a cluster defect may beeither the acceptor type or the donor type.

With this construction, in each forbidden band zone, the resonantwavelength of a point-like defect belonging to each forbidden band zoneis not included in the waveguide-transmittable wavelength band in theforbidden band zones adjacent thereto on the first reflecting side.Hence, in the case of an optical demultiplexer, light having thewavelength to be demultiplexed in the forbidden band zone but havingpassed over the point-like defect without being introduced there cannotpropagate the waveguide of the adjacent forbidden band zone on the sideof the first reflecting section, but is totally reflected on theboundary between the forbidden band zone and the adjacent forbidden bandzone. Light thus reflected returns to the point-like defect belonging tothe forbidden band zone. Hence, the optical demultiplexing efficiency atthe point-like defect in each of the forbidden band zones increasescompared to the case where no reflection occurs at the boundary betweenthe forbidden band zones. In the case of an optical multiplexer, of alllight with the resonant wavelength of the point-like defect introducedinto the waveguide from the point-like defect in each of the forbiddenband zone, light propagating toward the first reflecting section, whichis present on the side opposite to the side where light is taken out, istotally reflected at the boundary with the adjacent forbidden band zone,and propagates toward the side where light is taken out. Hence, themultiplexing efficiency also increases.

In each of the forbidden band zones, by appropriately setting thedistance between the boundary of the forbidden band zone with theadjacent one on the first reflecting section side and the point-likedefect in the forbidden band zone, the demultiplexing efficiency or themultiplexing efficiency can be further increased. In the case of anoptical demultiplexer, it is preferable to set the distance so that thelight reflected on the point-like defect belonging to the forbidden bandzone and the light reflected on the boundary with the adjacent forbiddenband zone are attenuated by interference, that is, the phase differencebetween the two reflected lights is π. In the case of an opticalmultiplexer, it is preferable to set the distance so that the lightpropagating from the point-like defect toward the light take-out portside of the waveguide and the light propagating in the oppositedirection and reflected on the boundary with the adjacent forbidden bandzone on the other side are intensified by interference, that is, thephase difference between the two lights is 0.

Note that there is no adjacent forbidden band zone on the firstreflecting section side in the forbidden band zone to which the firstreflecting section belongs. Light propagating toward the firstreflecting section side is reflected on the first reflecting section.Hence, the distance between the point-like defect and the firstreflecting section is set in the forbidden band zone to which the firstreflecting section belongs. The condition for the setting is the same asthe condition for the distance between the point-like defect and theboundary with the adjacent forbidden band zone in other forbidden bandzones.

In the case of the second mode, as well as in the case of the firstmode, the demultiplexing efficiency can be improved by adjusting Qp/Qvin an optical demultiplexer. In the second mode, light with thewavelength to be demultiplexed is totally reflected on the boundary oftwo adjacent forbidden band zones. Hence, equation (1) obtained based onthe condition of total reflection on the first reflecting section in thefirst mode is established in each of the forbidden band zones in thesecond mode except for forbidden band zones provided with the firstreflecting section. This is always established in the construction ofthe second mode, which is different from the case of the first mode.With the construction that light having a predetermined wavelength istotally reflected on the first reflecting section adopted, equation (1)is established in all the forbidden band zones including one providedwith the first reflecting section.

The distance between the point of the waveguide nearest to thepoint-like defect and the boundary with an adjacent forbidden band zoneis determined so that the phase difference between light reflected onthe boundary with the adjacent forbidden band zone and light reflectedon the point-like defect is π. If the value of Qp/Qv is set in the rangeof 1.4 to 2.8 in each of the forbidden band zones in the same way asthat in the first mode, the demultiplexing efficiency can be 97% or morein any of the forbidden band zones. With Qp/Qv=2 in each of theforbidden band zones adopted, the demultiplexing efficiency in theforbidden band zone can be set to 100%.

Parameters associated with the other forbidden band zones do notcontribute to the demultiplexing efficiency in each forbidden band zone.Hence, it is only required to design each of the forbidden band zonesindependently so that the demultiplexing efficiency is maximized in theforbidden band zone.

By changing the cycle distance and the size of the modified refractiveindex areas and the size of the point-like defect in the same ratio, theresonant wavelength of the point-like defect can be controlled withoutaltering the Q-value or the like. Hence, if the optimal value of Qp/Qvis set by determining parameters of modified refractive index areas andthe point-like defect in one forbidden band zone, the resonantwavelength in each forbidden band zone can be easily set while theoptimal value of Qp/Qv is kept unchanged by magnifying or reducing theforbidden band zone in the same condition.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1( a) and 1(b) are plan views showing an example construction ofthe first mode according to the present invention of a two-dimensionalphotonic crystal optical multiplexer/demultiplexer using boundaryreflection.

FIG. 2 is a plan view showing another example construction of the firstmode of the two-dimensional photonic crystal opticalmultiplexer/demultiplexer using the boundary reflection.

FIG. 3 is a plan view showing an example construction of the second moderelating to the present invention of a two-dimensional photonic crystaloptical multiplexer/demultiplexer using boundary reflection and aschematic view showing the relationship between the transmission band ofa waveguide and the forbidden band zone with respect to the resonantfrequency.

FIG. 4 is a graph showing defect levels due to a donor-type clusterdefect obtained by embedding three modified refractive index areas in alinear arrangement.

FIG. 5 shows transmission and reflection of light in the case where thetwo-dimensional photonic crystal in the example construction of FIG. 3is used as an optical demultiplexer.

FIG. 6 shows transmission and reflection of light in the case where thetwo-dimensional photonic crystal in the example construction of FIG. 3is used as an optical multiplexer.

FIG. 7 shows five parameters for calculating the demultiplexingefficiency of a two-dimensional photonic-crystal demultiplexer usingboundary reflection according to the present invention.

FIGS. 8( a) and 8(b) show results of calculations of demultiplexingefficiencies in the case where Qp=Qv in an optical demultiplexer basedon a two-dimensional photonic crystal using boundary reflection.

FIG. 9 is a graph showing the demultiplexing efficiency over 2L/λ ofFIG. 8( a) as abscissa.

FIGS. 10( a) and 10(b) are graphs showing the spectral intensity oflight demultiplexed in the case where 2L/λ₀ is a half integer.

FIGS. 11( a) and 11(b) are graphs showing the spectral intensity oflight demultiplexed in the case where 2L/λ₀ is an integer.

FIGS. 12( a) and 12(b) are a representation and a graph showing resultsof calculations of demultiplexing efficiencies in the case where Qp=2Qvin a two-dimensional photonic crystal optical demultiplexer usingboundary reflection.

BEST MODE FOR CARRYING OUT THE INVENTION

(1) Example of a Construction According to the Present Invention of aTwo-dimensional Photonic Crystal Optical Multiplexer/demultiplexer UsingBoundary Reflection

FIG. 1 shows an example of a construction according to the presentinvention of the first mode of a two-dimensional photonic crystaloptical multiplexer/demultiplexer using boundary reflection. Vacancies12 each being a modified refractive index area are arranged in a body 11periodically in a triangular lattice pattern. A waveguide 13 is createdby rendering vacancies 12 defective in a linear arrangement. Both endsof the waveguide 13 reach ends of the body 11. In this example, nomember is provided at an end for propagation light to be reflectedthereon, and the end of the waveguide reaching the first end 15 of thebody serves as the first reflecting section 17, which reflects a part oflight propagating through the waveguide 13 due to the difference inrefractive index between the body and the air. On the other hand,introduction of propagation light into the wave guide (in the case of anoptical demultiplexer) or taking-out of the propagation light (in thecase of an optical multiplexer) is conducted at the second end 16 at theother side of the body to the first end 15. Note that the second end 16of the body reflects part of the propagation light in the waveguide in asimilar way to that on the first end 15 of the body.

A point-like defect is provided at a position in the vicinity of thewaveguide 13 and spaced by a predetermined distance L from the first end15 of the body. FIG. 1( a) shows an example provided with anacceptor-type point defect 141 and FIG. 1( b) shows an example providedwith a donor-type cluster defect 142. Distance L is the distance betweenthe point-like defect and the first end 15 of the body and distance L′is the distance between the point-like defect and the second end 16 ofthe body.

FIG. 2 shows another example of the first mode. A two-dimensionalphotonic crystal 21 not transmitting light with the resonant wavelengthof the point-like defect 14 therethrough is connected to the first end15 of the body. With such a construction, light with the resonantwavelength of the point-like defect 14 is totally reflected on the firstend 15 of the body.

By appropriately setting parameters such as the distances L and L′ andreflectance on both ends of the waveguide, optical multiplexingefficiency and optical demultiplexing efficiency can be increasedcompared to conventional cases. In the case where the first reflectingsection is in contact with the air as shown in FIG. 1, demultiplexingefficiency is increased by setting the distance L to the value n/2 times(wherein n is a positive integer) the resonant wavelength λ₀ of thepoint-like defect. This is because light reflected on the end of thewaveguide at the first end 15 side of the body without altering thephase, and light reflected on the point-like defect while reversing thephase are attenuated by interference in the waveguide 13 between thepoint-like defect and the second end 16 side of the body. On the otherhand, in multiplexing, the multiplexing efficiency is increased bysetting the distance L to the value n/2 times the resonant wavelength ofthe point-like defect. This is because light propagating directly on thewaveguide from the point-like defect to the second end 16 of the bodyand light propagating on the waveguide to the second end 16 afterreflected on the first end 15 of the body are intensified byinterference.

Note that λ₀ in the above description is the wavelength of light whilepropagating through the waveguide, which is made from a refractive indexmaterial, and is different from the wavelength λ of light in the airwhen light is demultiplexed from the point-like defect.

FIG. 3 shows an example of a construction of the second mode of atwo-dimensional photonic crystal optical multiplexer/demultiplexer usingboundary reflection. An optical multiplexer shown in the left of FIG. 3has a heterostructure consisted of plural forbidden band zones. In thisexample, the cycle distance a₁, a₂, a₃, . . . of the vacancies 32 inrespective forbidden band zones 301, 302, 303, . . . are set so thata₁>a₂>a₃> . . . . A waveguide 33 is created by rendering vacancies 32defective in a linear arrangement so as to pass through all theforbidden band zones. Donor-type cluster defects 341, 342, 343, . . .consisted of three linear vacancies are formed in the vicinity of thewaveguide 33 in respective forbidden band zones 301, 302, 303, . . . .

FIG. 4 shows resonant frequencies of the donor-type cluster defectsconsisted of three linear vacancies calculated by the plane-waveexpansion method. Note that details of the calculation are shown inJapanese Unexamined Patent Application No. 2003-279764. The ordinate inthe figure is assigned to the normalized frequency obtained as anon-dimensional value by multiplying the frequency of light with a/c(wherein a is the cycle distance of the modified refractive index areas,and c is the velocity of light). A single defect level 42 exits in atransmission band 41 (in the range of 0.267 to 0.280 in normalizedfrequency) of the waveguide. The value of the defect level 42 is about0.267 (in normalized frequency) and corresponds to a level in thevicinity of an end of the waveguide transmission band 41. Resonantfrequencies in the donor-type cluster defects 341, 342, 343, . . .consisted of three linear vacancies can be obtained by multiplyingnormalized frequencies of the defective levels 42 with c and then bydividing the products with the cycle distances a₁, a₂, a₃, . . . of thisexample.

The right part of FIG. 3 schematically shows a relationship in eachforbidden band zone between the transmission band and the resonantfrequency of the waveguide. In this example, since defect levels are inthe vicinity of an end of the waveguide transmission band, the defectlevel 52 in any forbidden band zone is included in the waveguidetransmission band 51 of the adjacent forbidden band zone on the lightintroduction and take-out section 36 side of the waveguide, but notincluded in the waveguide transmission band 51 of an adjacent forbiddenband zone on the other side of the waveguide from the lightintroduction/take-out section 36 side thereof. For example, the defectlevel f₂ of the forbidden band zone 302 is included in the waveguidetransmission band of the forbidden band zone 301, which is located onthe light introduction/take-out section 36 side, but not included in thewaveguide transmission band of the forbidden band zone 303 on the otherside of the waveguide from the light introduction and take-out section36.

Therefore, light with the resonant frequency of a donor type clusterdefect consisted of three linear vacancies in each of the forbidden bandzones can pass through the waveguide as far as the forbidden band zonefrom the light introduction section 36 and can reach this donor-typecluster defect consisted of three linear vacancies. On the other hand,light passing through this donor-type cluster defect consisted of threelinear vacancies and further propagating through the waveguide (whichwould be a loss in a conventional technique) cannot propagate throughthe adjacent forbidden band zone, is reflected on the boundary surfaceand again reaches this donor-type cluster consisted of three linearvacancies. For example, as is shown in FIG. 5, light with a frequency f₂transmitted through the waveguide 33 in an optical demultiplexer is, asshown with a thick solid line, introduced into the donor-type clusterdefect 342 consisted of three linear vacancies. A part of light with thefrequency f₂ passes over the defect 342 and further propagates forwardin the waveguide, but is not transmitted through the waveguide of theforbidden band zone 303; therefore, this part of light is reflected onthe boundary surface 352 again to reach the defect 342 (see thick brokenlines in FIG. 5). In this way, a loss caused by allowing light withresonant frequencies to be transmitted through the donor-type clusterdefects 341, 342, 343, . . . consisted of three linear vacancies issuppressed, thereby enabling the demultiplexing efficiency of light ineach defect to be improved.

In the case where the example of FIG. 3 is used as an opticalmultiplexer as well, efficiency can be increased. Light, which is a partof light multiplexed at a linear donor-type cluster defect andpropagates to the other side of the waveguide from the lightintroduction/take-out section 36, is, as shown in FIG. 6, reflected onthe boundary surface of a forbidden band zone (see thick broken lines inFIG. 6). Hence, all of light multiplexed from a defect reaches the lightintroduction/take-out section 36 of the waveguide.

Note that in the case of an optical demultiplexer, light reflected onthe boundary surface of a forbidden band zone sometimes passes throughas far as the light introduction/take-out section 36 without entering alinear donor type cluster defect, resulting in the demultiplexingefficiency of less than 100%. Therefore, it is necessary toappropriately set the distance between a defect and the boundarysurface, or the like parameter as described later.

While a linear donor cluster defect can be constituted of two, four ormore vacancy defects, it is desirable, as described above, to use adonor-type cluster defect consisted of three linear vacancies forming asingle defect level in the vicinity of an end of a waveguidetransmission band.

(2) Calculation of Demultiplexing Efficiency in the OpticalDemultiplexer Based on a Two-dimensional Photonic Crystal Using BoundaryReflection According to the Present Invention

The demultiplexing efficiency of an optical demultiplexer according tothe present invention is shown below as calculated on the basis of themode coupling theory. While the following description will be givenbased on the construction of an optical demultiplexer of the first modeshown in FIGS. 1( a), 1(b) and 2, the following result is also obtainedin a heterostructure optical demultiplexer of the second mode in thesame way as that in the optical demultiplexer of the first mode for eachof the forbidden band zones.

Five amplitudes of light A, S₊₁, S⁻¹, S₊₂ and S⁻² are used asparameters. As shown in FIG. 7, A is an amplitude of light with theresonant wavelength λ₀ demultiplexed from the point-like defect 72, S₊₁is an amplitude of light with the wavelength λ₀ propagating toward thepoint-like defect 72 in the waveguide 711 between the first end section73 of the body and the point-like defect 72, S⁻¹ is an amplitude oflight with the wavelength λ₀ propagating toward the first end 73 side ofthe body in the waveguide 711, S₊₂ is an amplitude of light with thewavelength λ₀ propagating toward the point-like defect 72 side in thewaveguide 712 between the second end 74 of the body and the point-likedefect 72, and S⁻² is an amplitude of light with the wavelength λ₀propagating toward the second end 74 of the body in the waveguide 712.Intensity reflectance on the first end 73 of the body and on the secondend 74 of the body is indicated by R₁ and R₂, respectively, andamplitude reflectance is indicated by r₁ and r₂, respectively. Moreover,Q-value between the waveguide 71 and the point-like defect 72 isindicated by Qp, and Q-value between the point-like defect 72 and thefree space is indicated by Qv.

With the mode coupling theory applied, relationships among the fiveparameters A, S₊₁, S⁻¹, S₊₂ and S⁻² are expressed by three equations.Two equations are derived with respect to reflection on the first end 73of the body and the second end 74 of the body. By solving thesimultaneous equations to calculate the five parameters, thedemultiplexing efficiency is obtained from the value of A.

FIGS. 8( a) and 8(b) to FIGS. 11( a) and 11(b) show results ofcalculation in the case where Qp=Qv. The condition of Qp=Qv gives themaximum demultiplexing efficiency of 50% in a conventionaltwo-dimensional photonic crystal optical demultiplexer in which noconsideration is given to boundary reflection.

FIG. 8( a) shows the demultiplexing efficiency of a demultiplexer in thecase where the intensity reflectance R₁ is 1 and the intensityreflectance R₂ is 0. In the first end 73 of the body, light is reflectedby a metal mirror while its phase is reversed. Hence, the amplitudereflectance r₁ is −1. Note that the ordinate is assigned to 2L/λ asobtained by multiplying the distance L with 2 and then dividing theproduct with the wavelength λ, while the abscissa is assigned to 2L′/λas obtained by multiplying the distance L′ with 2 and then dividing theproduct with the wavelength λ. In FIG. 8( a), the demultiplexingefficiency does not depend on the distance L′ and exhibits a constantvalue. In the description below, attention is paid to the distance L.FIG. 9 is a graph showing the demultiplexing efficiency with theabscissa assigned to 2L/λ (2L′/λ is an arbitrary value in the range ofcalculation of FIG. 8( a)). The demultiplexing efficiency when 2L/λ is ahalf integer is about 88%. This value is higher than the maximumdemultiplexing efficiency of 50% in a conventional two-dimensionalphotonic crystal optical demultiplexer. The reason why is consideredthat light reflected on the end 74 of the body in the waveguide 711 andlight reflected on the point-like defect 72 attenuate each other byinterference to thereby increase then amplitude of light demultiplexedfrom the point-like defect 72. For the reason contrary to that, thedemultiplexing efficiency is 0% when 2L/λ is an integer.

FIG. 8( b) shows the demultiplexing efficiency of the demultiplexer inthe case where the intensity reflectance R₁ is 1 and the intensityreflectance R₂ is 0.18. It is assumed in the calculation that light isreflected on a metal mirror on the first end 73 of the body and on theair on the second end 74 of the body. The value of the R₂ is obtainedfrom experiments on reflection of light on the boundary between the bodyand the air. An amplitude reflectance r₁ is −1 in the same way as thatin the case of FIG. 8( a). On the other hand, since the phase of lightdoes not change by reflection on the second end 73 of the body, anamplify reflectance r₂ is adopted as +(0.18)^(0.5). The demultiplexingefficiency in FIG. 8( b) also depends on the distance L′ as well. Thedemultiplexing efficiency in FIG. 8( b) is further increased compared tothe case of FIG. 8( a) and reaches 100% at that condition when theordinate and abscissa are represented both by half integers.

FIGS. 10( a), 10(b), 11(a) and 11(b) show spectral intensities ofdemultiplexed light in a point-like defect with the resonant wavelengthof 1.5 μm (the wavelength when being taken out into air) in the casewhere intensity reflectance R₁ and R₂, and amplitude reflectance r₁ andr₂ are the same as those in FIG. 8( b). In the case of FIG. 10( a) where2L/λ₀ and 2L′/λ₀ are both half integer, the intensity of light taken outfrom a point-like defect is 100% at the median of resonant wavelength.In the case of FIG. 10( b) where 2L/λ₀ is a half integer and 2L′/λ₀ isan integer, the intensity of light taken out from the point-like defectis as low as about 60% at the median of resonant wavelength, while being100% at the wavelength slightly shifted therefrom. In both cases ofFIGS. 11( a) and 11(b) where 2L/λ₀ is an integer, the intensity is 0% atthe median of resonant wavelengths.

FIGS. 12( a) and 12(b) show results of calculation in the case whereQp=2Qv. The other parameters except Q-value are the same as in the caseof FIG. 8( a) and FIG. 9 (R₁=0, R₂=0, r₁=−1). FIG. 12( a) shows arepresentation exhibiting the demultiplexing efficiency wherein theordinate is assigned to 2L/λ, while the abscissa is assigned to 2L′/λ.FIG. 12( b) is a graph of the demultiplexing efficiency, wherein theabscissa is assigned to 2L/λ (2L′/λ is an arbitrary value in the rangeof calculation in FIG. 12( a)). The demultiplexing efficiency does notdepend on L′ as in the case of Qp=Qv. On the other hand, thedemultiplexing efficiency is 100% when 2L/λ is a half integer in thiscase different from the case of Qp=Qv. Hence, by setting Qp=2Qv, thedemultiplexing efficiency can be obtained as 100% without providing asecond reflecting section as in the case of FIG. 8( b), and further,without imposing a specific limitation on L′.

1. A two-dimensional photonic crystal optical multiplexer/demultiplexerusing boundary reflection, comprising: a) a slab-shaped body; b) pluralmodified refractive index areas arranged periodically in the body, eachhaving a refractive index different from that of the body; c) awaveguide formed by creating defects of the modified refractive indexareas in a linear arrangement, the end of which is located on an end ofthe body; d) a point-like defect formed by creating a defect of modifiedrefractive index area or areas in the vicinity of the waveguide; and e)a first reflecting section provided at an end of the waveguide, forreflecting light having wavelength equal to the resonant wavelength ofthe point-like defect by connecting another two-dimensional photoniccrystal not transmitting light with the wavelength to the end of thebody.
 2. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer using boundary reflection according to claim1, wherein the distance between the first reflecting section and thepoint-like defect is set so that the phase difference between lighthaving wavelength equal to the resonant wavelength of the point-likedefect and reflected on the point-like defect, and light with the samewavelength passing over the point-like defect and reflected on the firstreflecting section is π.
 3. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer using boundary reflection according to claim1, wherein the distance between the first reflecting section and thepoint-like defect is set so that the phase difference between lighthaving wavelength equal to the resonant wavelength of the point-likedefect and introduced into the waveguide from this point-like defect,and light with the same wavelength and reflected on the first reflectingsection is
 0. 4. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer using boundary reflection according claim 1,wherein a second reflecting section reflecting at least part of lighthaving wavelength equal to the resonant wavelength is formed at the endof the waveguide opposite to the first reflecting section.
 5. Thetwo-dimensional photonic crystal optical multiplexer/demultiplexer usingboundary reflection according to claim 4, wherein the distance betweenthe second reflecting section and the point-like defect is set so thatthe phase difference between light with the resonant wavelength in thepoint-like defect and introduced from the second reflecting sectionside, and light having wavelength equal to the same wavelength,introduced from the second reflecting section, reflected on thepoint-like defect, and further reflected on the second reflectingsection is
 0. 6. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer using boundary reflection according to claim1, wherein light having wavelength equal to the resonant wavelength ofthe point-like defect is totally reflected on the first reflectingsection, and the ratio Qp/Qv is set in the range of 1.4 to 2.8 where Qpis the coupling coefficient between the point-like defect and thewaveguide, and Qv is the coupling coefficient between the point-likedefect and the air.
 7. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer using boundary reflection according to claim6, wherein the ratio of Qp/Qv is set to
 2. 8. A two-dimensional photoniccrystal optical multiplexer/demultiplexer using boundary reflection,comprising: a) a slab-shaped body; b) two or more forbidden band zonesprovided in the body; c) plural modified refractive index areas providedin each of the forbidden band zones, each area having a refractive indexdifferent from that of the body, and periodically arranged in the bodyin a different cycle distance from each other in each of the forbiddenband zones; and d) a waveguide formed by creating defects of modifiedrefractive index areas in a linear arrangement in the respectiveforbidden band zones, and passing through all the forbidden band zones;e) a point-like defect created in the vicinity of the waveguide in eachof the forbidden band zones; and wherein, f) a part of awaveguide-transmittable wavelength band in each of the forbidden bandzone is not included in a waveguide-transmittable wavelength band of allforbidden band zones present on one side of the forbidden band zone, butincluded in the waveguide-transmittable wavelength band of all forbiddenband zones present on the other side of the forbidden band zone; and g)the resonant wavelength of the point-like defect created in each of theforbidden band zones is included in the part of the transmissionwavelength band.
 9. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer using boundary reflection according to claim8, wherein the point-like defect is a linear donor-type cluster defectformed by rendering three adjacent modified refractive index areasdefective.
 10. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer using boundary reflection according to claim8, wherein the end of the waveguide of said one side is located on anend of the body, and another two-dimensional photonic crystal nottransmitting light having wavelength equal to the resonant wavelength ofthe point-like defect is connected to the end of the body.
 11. Thetwo-dimensional photonic crystal optical multiplexer/demultiplexer usingboundary reflection according to claim 8, wherein, the distance betweenthe boundary with the adjacent forbidden band zone on said one side andthe point-like defect provided in that forbidden band zone is set sothat the phase difference between light having wavelength equal to theresonant wavelength of the point-like defect of the forbidden band zoneand reflected on the point-like defect, and light with the samewavelength passing over the point-like defect and reflected on theboundary between the forbidden band zones is π.
 12. The two-dimensionalphotonic crystal optical multiplexer/demultiplexer using boundaryreflection according to claim 8, wherein the distance between theboundary with the adjacent forbidden band zone on said one side and thepoint-like defect provided in that forbidden band zone is set so thatthe phase difference between light with the resonant wavelength of thepoint-like defect of the forbidden band zone, and introduced into thewaveguide from this point-like defect, and light with the samewavelength and reflected on the boundary between the forbidden bandzones is
 0. 13. The two-dimensional photonic crystal opticalmultiplexer/demultiplexer using boundary reflection according to claim8, wherein the ratio Qp/Qv is set in the range of 1.4 to 2.8, where Qpis a coupling coefficient between the point-like defect and thewaveguide in each of the forbidden band zones and Qv is a couplingcoefficient between the point-like defect and the air.
 14. Thetwo-dimensional photonic crystal optical multiplexer/demultiplexer usingboundary reflection according to claim 13, wherein the ratio of Qp/Qv isset to 2.